Relationships between uptake of [68Ga]Ga-DOTA-TATE and absorbed dose in [177Lu]Lu-DOTA-TATE therapy

Background Somatostatin receptor 68Ga PET imaging is standard for evaluation of a patient’s suitability for 177Lu peptide receptor radionuclide therapy of neuroendocrine tumours (NETs). The 68Ga PET serves to ensure sufficient somatostatin receptor expression, commonly evaluated qualitatively. The aim of this study is to investigate the quantitative relationships between uptake in 68Ga PET and absorbed doses in 177Lu therapy. Method Eighteen patients underwent [68Ga]Ga-DOTA-TATE PET imaging within 20 weeks prior to their first cycle of [177Lu]Lu-DOTA-TATE. Absorbed doses for therapy were estimated for tumours, kidney, spleen, and normal liver parenchyma using a hybrid SPECT/CT–planar method. Gallium-68 activity concentrations were retrieved from PET images and also used to calculate SUVs and normalized SUVs, using blood and tissue for normalization. The 68Ga activity concentrations per injected activity, SUVs, and normalized SUVs were compared with 177Lu activity concentrations 1 d post-injection and 177Lu absorbed doses. For tumours, for which there was a variable number per patient, both inter- and intra-patient correlations were analysed. Furthermore, the prediction of 177Lu tumour absorbed doses based on a combination of tumour-specific 68Ga activity concentrations and group-based estimates of the effective half-lives for grade 1 and 2 NETs was explored. Results For normal organs, only spleen showed a significant correlation between the 68Ga activity concentration and 177Lu absorbed dose (r = 0.6). For tumours, significant, but moderate, correlations were obtained, with respect to both inter-patient (r = 0.7) and intra-patient (r = 0.45) analyses. The correlations to absorbed doses did not improve when using 68Ga SUVs or normalized SUVs. The relationship between activity uptakes for 68Ga PET and 177Lu SPECT was stronger, with correlation coefficients r = 0.8 for both inter- and intra-patient analyses. The 177Lu absorbed dose to tumour could be predicted from the 68Ga activity concentrations with a 95% coverage interval of − 65% to 248%. Conclusions On a group level, a high uptake of [68Ga]Ga-DOTA-TATE is associated with high absorbed doses at 177Lu-DOTA-TATE therapy, but the relationship has a limited potential with respect to individual absorbed dose planning. Using SUV or SUV normalized to reference tissues do not improve correlations compared with using activity concentration per injected activity. Supplementary Information The online version contains supplementary material available at 10.1186/s13550-022-00947-2.

(NETs) [1,2] is typically preceded by SSTR-PET imaging using [ 68 Ga]Ga-DOTA-TATE or -TOC to ensure adequate receptor expression [3,4]. The use of a theragnostic approach with the same or similar peptides for imaging and therapy offers opportunities for therapy stratification, but there is today no consensus on the predictive value of 68 Ga-SSTR-PET/CT imaging with respect to response, absorbed doses, or activity uptakes in tumours and normal organs for therapy. A number of studies have investigated the relationship between SSTR expression quantified from 68 Ga-SSTR-PET/CT and the outcome of [ 177 Lu]Lu-DOTA-TATE or -TOC therapy of NETs [5][6][7][8][9][10]. When examining such relationships, it is often implicitly assumed that a high tumour uptake in pretherapeutic 68 Ga-SSTR-PET/CT images also infers high tumour uptake and absorbed dose during 177 Lu therapy.
To the best of our knowledge, there is to date only one study that made a direct, quantitative comparison of results from [ 68 Ga]Ga-DOTA-TOC PET and absorbed doses delivered during [ 177 Lu]Lu-DOTA-TOC therapy for NET patients [11]. In that study, tumour dosimetry was performed for 21 patients based on serial planar 177 Lu imaging, and a statistically significant correlation (r = 0.7) was found between the 68 Ga-SUV (SUV mean or SUV max ) and the 177 Lu absorbed dose [11]. Furthermore, a few reports on similar radiopharmaceuticals or indications are available. Krebs et al. [12] reported on the treatment of 20 NET patients using a SSTR antagonist ( 177 Lu-satoreotide tetraxetan) with pre-therapeutic 68 Ga-imaging and 177 Lu dosimetry based on a hybrid SPECT-planar method. Various quantitative parameters were analysed, including tumour-to-normal-tissue SUV ratios, and the highest correlation (r = 0.5) was found between 68 Ga-SUV peak and the 177 Lu absorbed dose to lesions [12]. Hänscheid et al. [13] reported data from 11 patients treated for meningioma, where 177 Lu dosimetry was performed with a hybrid SPECT-planar method. They found that the 68 Ga-SUV max correlated well with the 177 Lu activity concentration 1 h after administration (r = 0.95), whilst the correlation to 177 Lu absorbed dose was moderate (r = 0.76). For [ 177 Lu]Lu-PSMA, pre-therapeutic 68 Ga-PET/CT and 177 Lu absorbed doses have also been compared, e.g. by Peters et al. [14].
Investigation of possible relationships between uptakes of 68 Ga-SSTR-PET and absorbed doses in 177 Lu PRRT can be made from different perspectives. In the abovementioned studies, the relationship was approached on a population level, reflecting the overall relationship across patients. For metastatic disease, analyses can also be made across the tumours within individual patients, addressing the distribution of uptakes and absorbed doses, i.e. whether a higher uptake of [ 68 Ga] Ga-DOTA-TATE in one tumour than another generally means that the absorbed dose is higher for that tumour in [ 177 Lu]Lu-DOTA-TATE therapy. Thirdly, the question can be posed as an estimation problem, to understand whether and how well absorbed doses in 177 Lu PRRT can be predicted from a pre-therapeutic 68 Ga-SSTR-PET. This perspective is relevant with regards to personalized dose planning, where both tumours and normal organs need to be considered. The various perspectives need to be considered separately, as they require different methods for evaluation.
Studies that compared the activity uptakes in 68 Ga-SSTR-PET/CT with the uptakes and absorbed doses in 177 Lu-PRRT have mainly used different variants of SUV for evaluation of the 68 Ga images. Besides SUV, different tumour-to-tissue ratios have been proposed, where reference tissues include the liver parenchyma, spleen, or blood [5,15,16]. Using SUV ratios is partly methodologically motivated, as this may partly mitigate the SUV dependence on factors such as reconstruction settings, the PET/CT system, and the accumulation time [17]. Another motivation is the pharmacokinetics, as demonstrated for 10 patients examined by dynamic [ 68 Ga] Ga-DOTA-TATE and -TOC PET/CT, leading to the suggestion of using the tumour-to-blood SUV ratio [16,18]. However, a simpler, and more fundamental parameter than SUV is the activity concentration. Although SUV is well established as a metric in diagnostics and patient selection from 68 Ga-SSTR-PET/CT [3,4], the reasons for using SUV are less evident when attempting to find a relationship to the therapeutic absorbed dose from 177 Lu. Specifically, the inclusion of the patient's weight can be questioned (SUV = activity concentration × weight/ injected activity), as the weight does not enter the calculation of the absorbed dose to tumours and organs.
The aim of this study was to investigate whether and how parameters derived from [ 68

Patient data
The patients included in this study are a subset of patients from the Iluminet trial [19], which was designed to study the safety and efficacy of dosimetry-based therapy with [ 177 Lu]Lu-DOTA-TATE in patients with welldifferentiated metastatic neuroendocrine tumours.

Activity preparation and administration
The labelling of [ 68 Ga]Ga-DOTA-TATE was performed using an established technique described in Gålne et al. [20]. Patients were prescribed an activity per body weight of 2.5 MBq/kg and received a total activity of (0.17 ± 0.04) GBq (mean ± standard deviation). The injected amount of peptide was (14 ± 6) nmol (equivalent to (20 ± 8) µg), and the fraction of the DOTA-TATE molecules that were radiolabelled was (1.3 ± 0.5) × 10 −4 . The radiochemical purity exceeded the lower limit of 91% for all administrations.

Ga PET imaging
PET/CT acquisitions were performed on a GE Discovery PET/CT 690. The time between injection and imaging was (64 ± 5) min. Images were acquired from head to mid-thigh, with acquisition time 3 min per bed position. Tomographic images were reconstructed with an in-plane matrix size of 192 × 192 and voxel size 3.65 × 3.65 × 3.27 mm 3 , using time-of-flight information and OS-EM with 3 iterations and 12 subsets, compensation for attenuation and scatter, three-dimensional pointspread function (PSF) modelling (referred to as VPFX-S on the camera system), a transaxial 5 mm full width at half maximum (FWHM) Gaussian post-filter, and an axial z-filter.

Lu SPECT imaging
SPECT/CT studies were acquired at nominally 1 d post-administration. For 17 patients the SPECT/CT was acquired (21.9 ± 1.1) h after administration, whilst one had the SPECT/CT performed at 94.6 h. To make SPECT-derived data consistent, the latter set of data were recalculated to the time point of the corresponding day one planar image (22.3 h) using the planar-derived effective half-lives for the respective tissues. The timing of the SPECT-derived data for all patients was then (21.9 ± 1.0) h after administration. Two systems were used, GE Discovery VH (1 patient) and GE Discovery 670 (17 patients). Both systems were equipped with mediumenergy collimators and projections were acquired in 60 angles over 360 • in 128 × 128 matrices with pixel sizes 4.02 × 4.02 mm 2 (Discovery VH) or 4.42 × 4.42 mm 2 (Discovery 670). An energy-window centred at 208 keV with a width of 20% (Discovery VH) or 15% (Discovery 670) was employed. Tomographic images were reconstructed using an off-line program using OS-EM with 10 subsets, including compensations for attenuation and scatter using the model-based ESSE scattercompensation method [22]. Since different steps in the image-based dosimetry method required SPECT images with different properties, three different reconstruction settings were used [23]. Briefly, the first type of SPECT image (ASR-8) was used for visual inspection and manual delineation of organs, and was reconstructed with resolution compensation and 8 iterations. The second type of SPECT image (AS-8) was used for automatic delineation of tumours, and was reconstructed without resolution compensation with 8 iterations. The third type of SPECT image (ASR-40) was used for activity and absorbed dose estimation, and was reconstructed with resolution compensation and 40 iterations.

Lu planar gamma camera imaging
Dosimetry for 177 Lu was performed using a hybrid SPECT-planar approach. For this purpose, planar wholebody gamma camera images were acquired at nominally 1 h, 24 h, 96 h, and 168 h post-injection (p.i.), using the same camera systems as for SPECT/CT. For each time point, anterior-posterior scans were co-registered to a scout radiograph and the geometric mean calculated on a pixel-by-pixel basis. Attenuation and scatter correction was performed using the scout radiograph to estimate the attenuation and scatter depth. This process yielded whole-body planar images with pixel values in projected activity [24].

Camera calibration
The PET camera system was calibrated for 18 F against the activity meter once every three months, and 18 F SUV verification measurements were made at least once per month. Retrospectively, SUV measurements were also made for 68 Ga. The SUV for 18 F was obtained to (0.99 ± 0.03) g mL −1 , while for 68 Ga it was (0.94 ± 0.02) g mL −1 A similar systematic SUV deviation from 1.00 g mL −1 for 68 Ga has been reported by others [25,26]. In this work, the observed deviation was considered in the PET imagebased quantification by division of the activity concentrations from volumes of interest (VOIs) by the factor 0.94. The gamma camera was calibrated for 177 Lu by measurement of the system sensitivity in air [27], which was used for both planar and SPECT image calibration.

Quantification of the activity concentration
For both PET and SPECT images, VOIs were delineated over organs and tumours and recovery coefficients (RCs) applied, as described below. Activity concentrations were calculated as the total activity in the VOI divided by the VOI volume (SPECT) or the mean value in the VOI (PET), divided by the relevant RC. All data were normalized to the injected activity and decay-corrected to the time of administration using the physical half-lives of 68 Ga or 177 Lu [28,29], giving the activity concentration per injected activity, henceforth referred to as AC/ IA. SUV values (SUV max and SUV mean ) were calculated according to clinical practice, i.e. based on non-partialvolume corrected activity concentrations, decay-corrected to the time of injection, normalized to the injected activity, and multiplied by the body weight. For SUV max the maximum voxel value in the VOI was used.

Image segmentation Organ delineation
For left and right kidney, liver parenchyma, and spleen VOIs were manually defined in the SPECT/CT and PET/ CT images. For spleen and kidneys, whole-organ VOIs were defined mainly using the CT for guidance, although, in case of misalignment between the CT and SPECT or PET, the VOIs were adjusted. For liver parenchyma, multiple small VOIs were defined with the ambition to avoid tumour-infiltrated liver. For PET/CT images, the blood activity concentration was quantified by placing a small VOI in 10 consecutive transverse planes in the descending aorta, taking care to avoid regions close to lesions or lymph nodes with high activity uptakes. For planar images, small regions of interest were drawn centrally in the respective organ, with a margin to the organ contour to avoid interference from activity in neighbouring tissues.

Tumour delineation
To be eligible for assessment, a given tumour had to be well identifiable in both PET and SPECT images. To be suitable for hybrid planar-SPECT/CT time-activity analyses a further requirement was limited signal overlap from activity in surrounding tissues, and a set of criteria for tumour inclusion, detailed in Roth et al. [23,30], were applied.
For planar images, tumour delineation was performed using a semiautomatic active rays-based technique [30]. For SPECT and PET images, a semiautomatic method based on Fourier surfaces was applied [31]. Tumours were manually identified by defining a rough VOI around the tumour with a margin. For SPECT, the ASR-8 images were used for manual selection and the Fourier surface method was then applied on the AS-8 images. For PET images, the clinical reconstructions were used for both manual identification and the subsequent automatic delineation. A few delineations were modified after review by the responsible oncologist.
The Fourier surface method has been previously validated for tumour segmentation in 177 Lu SPECT images by Gustafsson et al. [31], where it was found that reconstruction using AS-8, i.e. without resolution recovery, gave good performance in terms of volume preservation. To evaluate the performance for the PET images from the camera system used in this work, experimental data from Jönsson et al. [32] were used. These included PET/CT images of six 68 Ga-filled spheres in a NEMA IEC Body Phantom with volumes between 0.52 mL and 26.5 mL, and background-to-sphere activity concentration ratios of 0%, 20%, 40%, 60%, and 80%. At application of the Fourier surface segmentation method to these images, a systematic negative bias in the volumes was obtained, likely as a result of the resolution recovery included in the reconstruction. To correct for this volume error, the physical sphere volume V p was mapped to the volume estimated from segmentation, V s , and the backgroundto-object activity concentration ratio, η , following where a 0 , a 1 , a 2 , and a 3 are parameters determined through linear regression. At application for determination of tumour volumes and activity quantification from patient PET images, Eq. 1 was used as a post-segmentation correction, such that V s and η was determined from the images, and the tumour volume obtained as V p , as described in Appendix.

Partial-volume correction
As the general blood activity concentration differed substantially between 1 h and 24 h after DOTA-TATE administration, the image contrast and general background level differed between the 68 Ga-PET and 177 Lu-SPECT images. Moreover, the spatial resolution of the two modalities differed. For these reasons, different strategies were required for partial-volume correction (PVC).

PVC of organ data
For SPECT, kidneys and spleen were corrected for spillout using an RC of 0.85, as previously determined for kidneys and spleen [27,33]. The RC applied for liver parenchyma was unity, since the VOIs used were substantially smaller than the organ extension.
For PET, the RCs for kidneys and spleen were determined for each separate VOI, by convolving the VOI mask with the PSF of the reconstructed images. The PSF was determined using matched filter analysis [34] applied to the 68 Ga sphere phantom data described above. The FWHM of the Gaussian PSF was determined to 6.4 mm (isotropic). The RC for liver parenchyma was unity.

PVC of tumour data
For 177 Lu-SPECT, compensation for spill-out of object signal was made using a previously reported expression of the RC as a function of volume, R V p following where α and β are two fitting parameters [23,31,35]. These parameters were determined based on sphere phantom experiments with V p representing the physical sphere volumes [23]. At application of Eq. 2 for PVC and activity quantification of patient tumours, the volumes obtained from the Fourier surface segmentation were applied [31]. For the 68 Ga-PET images, with a comparably high blood background level, both the spill-out of object signal and spill-in from background were considered. The 68 Ga sphere phantom data from Jönsson et al. described above were used to establish the recovery for the camera system used. In these images, spherical VOIs were defined with volumes according to the physical sphere volumes, V p . The recovery was calculated as the apparent activity concentration in the respective VOI, divided by the activity concentration from phantom preparation. The RC was parametrized according to where R 0 V p is the RC expression in Eq. 2, η is the background-to-object activity concentration ratio, and f is a fitting parameter in the interval f ∈ [0, 1] . For a nonradioactive background then R V p , 0 = R 0 V p , i.e. the same expression as in Eq. 2. When the activity concentration in the object and background are identical then R V p , 1 ≡ 1 . The values of α , β and f were obtained by fitting Eq. 3 to the phantom data, using nonlinear least squares with Levenberg-Marquardt's method [36]. The fitted function R V p , η is shown in Appendix, where the application of Eq. 3 is also described.

Absorbed dose calculation for 177 Lu
The time-sequence of planar images were used to estimate the shape of the time-activity curves. Region-specific, relative activity values were calculated as the mean signal per pixel in the ROIs. For organs, background correction was applied by subtracting the mean signal in a ROI placed over the patient's thigh, assumed to represent an unspecific, general body background. For tumours, the average of the five highest pixel values within the ROI was used [30]. Curve fitting of the activity versus time data was performed using unweighted nonlinear least squares. For organs, a mono-exponential function was fitted to the last three time points, and a linear function between the first and second time point. For tumours, the curve consisted of a quadratic function between the first two time points and a mono-exponential function for the last three time points [23,30]. To calculate the absorbed dose, a Monte Carlo program based on the EGS4 code with PRESTA was used [37,38]. Absorbed dose rate images were calculated using the ASR-40 SPECT/CT images as input. Each VOI was applied to the volumeaveraged absorbed dose rate, which was then corrected using the relevant RC. Absorbed dose rate curves were obtained by rescaling the fitted time-activity curves to the absorbed dose rate, with a scaling factor determined from the curve value at the time of SPECT imaging. Finally, the absorbed dose was calculated by analytical integration of this rescaled curve. The assumption was thus made that the absorbed dose rate curves followed the time-activity curves [23]. For each of the segmented structures (organs and tumours), the absorbed dose per injected activity (AD/IA) was calculated.

Prediction of 177 Lu tumour absorbed doses from 68 Ga PET images
The possibility to predict tumour absorbed doses for [ 177 Lu]Lu-DOTA-TATE based on the [ 68 Ga]Ga-DOTA-TATE activity concentrations was explored. Based on previously published patient data, the assumption was made that the time-activity curves followed a monoexponential pattern, with effective half-lives of 103 h and 81 h for grade-1 and grade-2 NET patients, respectively [23]. The 68 Ga activity concentration from images was propagated back to the concentration at time t = 0 , and the corresponding 177 Lu activity concentration calculated by scaling to the injected activities, A inj,177Lu /A inj,68Ga . The predicted 177 Lu absorbed doses were then calculated by the assumption of electron local energy deposition [39], a tissue density of 1.04 g mL −1 , and integration of the mono-exponential time-activity curves. The predicted 177 Lu absorbed doses were compared with the absorbed doses measured at therapy.

Statistical analysis
For organs (kidneys, spleen, and liver parenchyma), the connection between the uptakes of [ 68 Ga]Ga-DOTA-TATE and the relevant dosimetric parameters for [ 177 Lu] Lu-DOTA-TATE were studied using Pearson's correlation coefficient. For kidneys, the mean of the data for left and right kidneys was considered to obtain independent data points.
For tumours, a cutoff volume was introduced, to exclude tumours with size close to the system spatial resolution [31]. Thus, tumours with volumes smaller than 5 mL as quantified from PET images were excluded from further analysis. Separate analyses were made of inter-and intra-patient correlations, using weighted correlation coefficients and repeated-measures correlations, respectively, as suggested by Bland and Altman [40,41]. For the weighted correlation, each patient contributed with a single data point in the form of the mean, and the correlation was calculated using the number of tumours per patient as weights. For the repeated-measures correlation, all tumour data were used. The slope was assumed to be common for all patients, while the intercept was treated as patient-specific in the linear fitting. Correlations for which p < 0.05 were considered statistically significant.
To investigate the stability of the correlation coefficients, a leave-one-out analysis was also made in which single data points were removed and the correlation analysis repeated. The leave-one-out analyses were performed for organ correlations and inter-patient correlations for tumours.
The agreement between tumour absorbed doses predicted from 68 Ga PET and those quantified from peri-therapeutic 177 Lu images was studied using a Bland-Altman plot. Since the errors were expected to scale with absorbed dose, the relative deviations were studied rather than the absolute deviations. To achieve symmetry of positive and negative deviations, the analysis was performed using the logarithms of the ratios. The mean deviation and 95% coverage intervals were calculated for the logarithmized ratios which were then transformed back to linear relative deviations.

Organ and tumour volumes
For kidneys and spleen, the mean relative difference (± standard deviation) between organ volumes determined from 177 Lu-SPECT and 68 Ga-PET images were obtained to (2 ± 10) % and (-1 ± 12) %, respectively.  volume above 5 mL were included for further analysis (n = 52). For these tumours, the relative deviations between 177 Lu-SPECT and 68 Ga-PET volumes were (20 ± 52) %. For volumes below the cutoff volume, there was an increasingly larger systematic volume deviation, where most 177 Lu-SPECT-derived volumes were larger than those derived from 68 Ga-PET. Figure 2 shows results for kidneys, spleen, and liver, including the 177 Lu absorbed dose (AD/IA) and activity concentration, 177 Lu-AC/IA, both as a function of the 68 Ga-AC/IA. The correlation coefficients, regression parameters, and intervals obtained for the correlation coefficient in the leave-one-out analysis (leave-one-out  Tables 1 and 2, where the correlation coefficients when using 68 Ga SUV mean as explanatory variable are also included.

Organ absorbed doses and activity concentrations
For kidneys and spleen, there were significant (p < 0.05) positive correlations for the 177 Lu-AC/IA with respect to both 68 Ga-AC/IA and 68 Ga SUV mean , but the LOOI for kidneys was large, indicating that the result was unstable. For the 177 Lu-AD/IA, correlations were only significant for spleen. All significant correlations had approximately r = 0.6. Figure 3 shows the 177 Lu-AD/IA for tumours, as a function of the 68 Ga-AC/IA, 68 Ga-SUV mean , 68 Ga-SUV max , and various ratios of 68 Ga-SUV mean . For the latter, reference tissues were blood, liver parenchyma, and spleen. Relationships when using 68 Ga-AC/IA, 68 Ga-SUV mean , or 68 Ga-SUV max as explanatory variable are shown as both inter-and intra-patient correlations. The different SUV ratios are only shown on an inter-patient basis since the normalization is not expected to affect the intra-patient relationships. A summary of the obtained correlation coefficients, regression parameters, and LOOIs are given in Table 2. Figure 4 and Table 3 show corresponding results when the 177 Lu-AC/IA is used as dependent variable.

Tumour absorbed doses and activity concentrations
The inter-patient analyses showed significant correlations, exceptions being the 177 Lu-AD/IA as a function of any of the 68 Ga-SUV ratios, and the 177 Lu-AC/IA as a function of SUV mean /SUV spleen . In general, the correlations were stronger for 177 Lu-AC/IA than for 177 Lu-AD/ IA. Using the various SUV ratios as explanatory variables yielded weaker inter-patient correlations and did generally not improve the intra-patient correlations compared to when using 68 Ga-AC/IA, SUV mean , or SUV max . The intra-patient analyses showed significant repeated-measures correlations, with the exception of 177 Lu-AD/IA as a function of SUV mean /SUV spleen . Thus, within a given patient, the variation in 68 Ga uptakes between tumours generally also translated to a difference in 177 Lu uptakes and absorbed doses. Figure 5 shows results of the Bland-Altman analysis of the agreement between tumour absorbed doses estimated from 68 Ga PET images and serial peri-therapeutic 177 Lu-imaging. On average, the 68 Ga-based estimates obtained was 11% higher than the 177 Lu absorbed doses measured at therapy, with a 95% coverage interval of − 65% to 248%. There were no discernible patterns associated with G1 or G2 NETs.

Discussion
In this study, we have investigated the relationship between uptakes of [ 68 Ga]Ga-DOTA-TATE quantified in PET images, and uptakes and absorbed doses to tumours and organs during subsequent treatment with [ 177 Lu] Lu-DOTA-TATE for NETs. In summary, for tumours we see a significant (p < 0.05), moderately strong (r = 0.71), relationship across patients between the activity concentration from 68 Ga-PET images and the absorbed dose from 177 Lu-PRRT. A stronger relationship is seen with respect to the 177 Lu activity concentration from SPECT images 24 h after injection. On an individual level, the ability to predict the 177 Lu absorbed dose to tumours based solely on a 68 Ga-PET image is limited, with a 95% coverage interval of − 65% to 248%.
The use of 68 Ga-SSTR-PET for correlation with outcome and prognosis of NETs has been investigated both in general and with respect to 177 Lu-PRRT [5][6][7][8][9][10]. However, the connection between 68 Ga-SSTR-PET uptakes and absorbed doses during therapy is less studied [11]. Even if absorbed dose is not a direct measure of treatment outcome and toxicity, it is an established parameter in other forms of radiotherapy and is being gradually Table 2 Results for tumours of the 177 Lu-AD/IA with respect to various PET-derived explanatory variables Correlation coefficients (r), p-value (p), coefficients for the linear equation (y = kx + m, presented as k/m) and leave-one-out interval (LOOI, min; max) better established also for radionuclide therapy [35,42,43]. Hence, we believe that an increased understanding of relationships between 68 Ga-SSTR imaging and absorbed doses in 177 Lu-PRRT fills an important gap. A fundamental difficulty for quantitative interpretation of pre-therapeutic 68 Ga-SSTR-PET with respect to the absorbed doses delivered during 177 Lu-PRRT lies in the different half-lives of 68 Ga and 177 Lu [44] (6.6 d versus 68 min [28,29]). 68 Ga-SSTR-PET is typically performed 1 h p.i. [4] while therapy with [ 177 Lu]Lu-DOTA-TATE extends over several days or weeks [39]. So although the ligand is identical, the time scales of the processes exploited with 68 Ga imaging and 177 Lu therapy are markedly different, limiting the accuracy for prediction of the  68 Ga-SUV mean , 68 Ga-SUV max , and various 68 Ga-SUV ratios. Data underlying the inter-patient analyses are the means across the tumours in each patient, whereas the intra-patient analyses are based on data for the separate tumours in each patient, as indicated by the different colours time-integrated activity and absorbed dose [45]. There are also other factors that differ between the 68 Ga-SSTR-PET and 177 Lu-PRRT, such as the method of administration (bolus versus extended infusion), and the fraction of the peptides that are radiolabelled which differs by nearly three orders of magnitude. At the same time, 68 Ga-SSTR-PET imaging is today clinically used as part of the patient-selection process for 177 Lu-PRRT, and hence, to some extent, a correlation is implicitly assumed.

Inter-patient correlations
For tumours, the strengths of the obtained correlations between uptakes of [ 68 Ga]Ga-DOTA-TATE and absorbed doses in 177 Lu-PRRT are on par with those reported previously for NET and meningioma [11,13], and higher than those reported for satoreotide tetraxetan [12]. Comparison between uptakes in [ 68 Ga]Ga-PSMA-11-PET and absorbed dose in therapy with 177 Lu-PSMA-617 have also shown similar correlations [14]. Importantly however, from such correlations on a group level, it cannot  68 Ga-SUV mean , 68 Ga-SUV max , and various 68 Ga-SUV ratios. For the intra-patient analyses, different colours represent different patients be directly inferred that the therapeutic absorbed doses can be predicted for the individual patient. Based on the presented approach for prediction, using the 68 Ga-PET activity concentration combined with populationbased effective half-lives for [ 177 Lu]Lu-DOTA-TATE for NETs, only rough estimates of the absorbed doses in the upcoming therapy are obtained (Fig. 5). Personalized treatment planning based on 68 Ga-PET imaging will thus require more elaborate approaches, such as the inclusion of pharmacokinetic modelling [46].
The poor agreement between absorbed dose estimates (Fig. 5) can partly be theoretically explained by the combination of a protracted therapeutic delivery and a measurement at 1 h p.i. [45]. As such, considerable dispersion is expected. However, in principle, the accuracy of a measurement method needs to be considered in relation to the requirements for the application, and the results in Fig. 5 could then still be informative in cases when only a rough estimate is necessary. Apart from mathematical and biological considerations, different absorbed dose calculation methods are also used for the PET-based estimation compared to the peri-therapeutic dosimetry. However, the benefit of full Monte Carlo simulations compared with using local energy-deposition is typically small for 177 Lu [39,47] and is not expected to be the major reason for the disagreement between the estimated values.
Among the organs, only spleen exhibits a significant correlation between the uptake of [ 68 Ga]Ga-DOTA-TATE and the absorbed dose in 177 Lu-PRRT (Fig. 2). For kidneys, considered the primary organ-at-risk for 177 Lu-PRRT, we see no significant relationship, one  For liver parenchyma, the estimation of the activity concentration suffers from practical challenges for VOI definition. Although small VOIs have been applied there is a risk that tumour may have been included, both due to spillover from adjacent tumours in the images and due to microscopic disease. Whether or not a patient is on treatment with long-acting SSA has, in previous publications, been observed to affect the liver uptake of [ 68 Ga]Ga-DOTA-TATE and only to a lesser degree the tumour uptake [20]. According to the same authors variable time intervals from the last SSA injection did not affect uptake. It is therefore unlikely that this factor contributed to the dispersion in data for the liver and the tumour-toliver ratio. The stronger correlations obtained between the 68 Ga and 177 Lu activity concentrations, compared to the 177 Lu absorbed dose (Table 1) were expected. Absorbed dose depends on a combination of initial activity uptake and excretion, while the activity concentration measured in 68 Ga-PET at 1 h almost exclusively reflects the initial activity uptake. The uptake measured in 177 Lu-SPECT at 24 h is less affected by the excretion than the absorbed dose is, which reduces the variability relative to the activity concentration at 1 h, measured in 68 Ga-PET.
Of interest, our results provide no support for using different types of normalization of the 68 Ga activity concentration to improve the relationship to absorbed dose in 177 Lu-PRRT, neither with respect to normalization to body weight, i.e. calculation of SUV, nor with respect to a reference tissue. In this study, SUVs were calculated according to clinical practice, with no PVC applied, which may in part affect the correlations obtained. However, in relation to the 177 Lu absorbed dose, there is no theoretical reason to normalize the activity concentration to body weight. Even if the body size, as an indirect measure of the plasma volume, may affect the activity uptake, this will act the same for diagnostics and therapy. Normalization to a reference tissue can in principle be motivated to cancel differences between receptor-bound activity and activity in blood in different patients. However, in our data such normalizations only increase the dispersion. The practical difficulties associated with the estimation of activity concentration or SUV in blood or liver parenchyma from 68 Ga-PET images need to be emphasized. In a static 68 Ga-PET image, blood SUV is associated with large uncertainties as it requires the measurement of low activity concentrations, which, in addition to the associated statistical variation, puts great demands on the accuracy of compensations for scattered and random coincidences. Thus, we believe that from both a theoretical and a practical point of view, it is preferable to study the AC/IA directly rather than normalized variants thereof.
For the correlation analyses for kidneys, the sensitivity to individual data points, as revealed by the leave-oneout analysis, should be noted ( Fig. 2 and Table 1). The correlations obtained are largely governed by one or two data points rather than reflecting a general trend, and the significant correlations should hence be interpreted cautiously. Similar instability was not found for tumours.
The analysis of tumour data is more complex than for organs because of the varying number of tumours per patient, for which independence cannot be assumed. For this reason, the problem of finding a relationship between the uptakes in 68 Ga-PET and the therapy is separated into two questions: 1) whether there is a relationship between patients when regarding the mean values for the tumours within each patient and 2) whether there is a relationship for the separate tumours within patients, following the methodology presented by Bland and Altman [40,41]. Regarding the inter-patient analysis, a moderate correlation is obtained for the 177 Lu-AD/IA as a function of 68 Ga-AC/IA, while a stronger correlation is obtained for the 177 Lu-AC/IA. This indicates that there is a group-level relationship between the uptake in 68 Ga-PET and the 177 Lu absorbed dose. The intra-patient analysis shows similar results, where the relationship is weaker for 177 Lu-AD/IA than for 177 Lu-AC/IA. This indicates that there is a correlation also within individual patients, i.e. on average a high 68 Ga uptake for a separate tumour also corresponds to a high absorbed dose in subsequent 177 Lu-PRRT. The two analyses are complementary, and it is concluded that there are statistically significant, but moderately strong, correlations both intra-and inter-patient.
Two important limitations of this study are the low number of included patients and the relatively permissive inclusion criterion of a [ 68 Ga]Ga-DOTA-TATE PET performed up to 20 weeks prior to PRRT. The patient population was, however, one of well-differentiated NET with a low Ki67-index, i.e. the likelihood of significant change in tumour volume over the given time interval is small. Furthermore, the actual median time from PET imaging to PRRT was 5 weeks, further reducing such a potential confounder. The dosimetry methods used in this study have been extensively validated in previous papers [27,30,31]. In principle, however, image-based dosimetry based on SPECT-only imaging would be preferable to the hybrid method used. Furthermore, the employed cutoff volume of 5 mL is of concern, partly because it reduces the number of included tumours, but also because it systematically excludes tumours with a certain characteristic which could theoretically lead to biased results. However, the uncertainties associated with estimated volumes (Fig. 1) and activity concentrations of structures with dimensions close to the system spatial resolution are well known [31]. Thus, excluding the smallest tumours was considered necessary not to contaminate the results.
In summary, we find that there is a statistical relationship between tumour uptake at [ 68 Ga]Ga-DOTA-TATE PET and absorbed dose to tumours in subsequent 177 Lu-PRRT, but that this association is moderate at best. Given that previous studies have shown correlations of approximately the same strength, methodological differences notwithstanding, we believe that these moderate correlations reflect the actual strength of the relationship, rather than being a result of measurement uncertainties. Furthermore, we find no, or unstable, relationships for organs, except for spleen. Thus, at the group level there are relevant relationships between the uptake in [ 68 Ga]Ga-DOTA-TATE PET and the upcoming 177 Lu-PRRT. However, to be able to practically use [ 68 Ga]Ga-DOTA-TATE PET for absorbed dose planning at the individual level, more complex models are needed that take patient-specific factors into account, beyond simple univariate analyses.

Conclusion
On a group level, a higher tumour uptake of [ 68 Ga] Ga-DOTA-TATE as measured from PET images 1 h p.i. is associated with higher absorbed doses in subsequent therapy with [ 177 Lu]Lu-DOTA-TATE. On an individual level, the predictive power of absorbed dose estimates is limited. Correlations are not improved by using 68 Ga SUV or normalized SUVs compared with using activity concentration per injected activity.